Q. 52 - Calculus

Question

Last night Phil went jogging along Main Street. His distance from the post office t minutes after $6:00$ p.m. is shown in the preceding graph at the right.

(a)  Give a narrative (that matches the graph) of what Phil did on his jog. 

(b)  Sketch a graph that represents Phil’s instantaneous velocity t minutes after $6:00$p.m. Make sure you label the tick marks on the vertical axis as accurately as you can.

 

(c)  When was Phil jogging the fastest? The slowest? When was he the farthest away from the post office? The closest to the post office? 

Step-by-Step Solution

Answer

Ans:   

(a)  Observing the graph it is clear that Phil has speed up his jogging for first $10-12$ minutes, then he slow down his speed for $40$ minutes. At $t=40$ he comes to rest and again he speeds up his jogging for the next $20$ minutes.

(b)   The graph of the velocity function.

(c)   Phil jogging fastest for first $10-12$ minutes. His jogging becomes slowest for $12-40$ minutes. He was farthest away from the post office at $t=12$ minutes and he was closest to the post office at $t=40$ minutes.

Step 1. Given information.

His distance from the post office $t$ minutes after $6:00$ p.m. is shown in the preceding graph at the right. 

Step 2. (a) Consider the graph, Here the objective is to give a narration of what Pill did on his jog.

Observing the graph it is clear that Phil has speed up his jogging for the first $10-12$ minutes, then he slow down his speed for $40$ minutes. $t=40$ he comes to rest and again he speed up his jogging for the next $20$minutes.

Step 3. (b) Here the objective is to draw the graph of Phil's velocity function for t minutes after 6 : 00 P M .

The graph of the velocity function can be drawn as follows:

Step 4. (c) Here the objective is to write when Phil jogging the farthest, the slowest, and farthest away from the post office, the closest to the post office.

Phil is jogging fastest for first $10-12$ minutes. His jogging becomes slowest for $12-40$ minutes. He was farthest away from the post office at $t=12$ minutes and he was closest to the post office at $t=40$ minutes.